"Game Embed Mode" causes problem with focus when debugging via DAP from external IDE

### Tested versions

- Reproducible in: Godot 4.6 (master branch)

### System information

All OS

### Issue description

When starting a game debug session from Rider using the Debug Adapter Protocol (DAP), the Godot game window does not automatically gain focus or appear in front.

### Steps to reproduce

1. Open a Godot project using Godot Editor 4.6.
2. Use Rider IDE with Godot DAP integration (or any IDE using DAP to debug GDScript).
3. Start a debug session from the IDE.
4. Observe that the game window launches but does not gain focus; the IDE remains focused.

If I disable the "Game Embed Mode" feature, focus would work as expected.

### Minimal reproduction project (MRP)

This can be reproduced with any minimal Godot project.

Related to https://youtrack.jetbrains.com/issue/RIDER-132058/Debug-GdScript-would-not-bring-the-game-to-front

Start by reproducing the issue in Godot 4.6 with Rider or another IDE using DAP, with Game Embed Mode enabled and disabled for comparison. Trace the editor's Game Embed Mode and debug-session window-focus handling; done means the game window reliably comes to the front when an external DAP session starts.

Written by the indexing model from the issue text.